Discrete Dynamics in Nature and Society
Volume 2005 (2005), Issue 1, Pages 87-92
doi:10.1155/DDNS.2005.87
A simple mathematical model for Batesian mimicry
Department of Mathematics and Statistics, Northern Arizona University, Flagstaff 86011, AZ, USA
Received 24 September 2003
Copyright © 2005 Terence R. Blows and Barry J. Wimmer. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
A simple mathematical model is presented for Batesian mimicry,
which occurs when a harmless species (mimic) is morphologically similar to another species (model) that is noxious or distasteful to predators, thus gaining a measure of protection. Although mathematical models for species interaction, such as predator-prey
or competition, are well known, there is no similar literature on mimicry. The mathematical model developed here is a one-dimensional iterated map which has the full range of dynamic behavior present in the logistic map, depending on the values of its parameters. The dynamics ranges from a stable fixed point and stable cycles through chaotic dynamics achieved through a sequence of period doubling bifurcations.